1. Field of the Invention
The present invention relates to atomic force microscopes (AFMs) and, more particularly, to an AFM and method of use thereof that dynamically controls the oscillating drive signal to the cantilever based on the amplitude of the measured response of the cantilever.
2. Description of the Related Art
An Atomic Force Microscope (xe2x80x9cAFMxe2x80x9d), as described in U.S. Pat. No. RE 34,489 to Hansma et al. (xe2x80x9cHansmaxe2x80x9d), is a type of scanning probe microscope (xe2x80x9cSPMxe2x80x9d). AFMs are high-resolution surface measuring instruments. Two general types of AFMs include contact mode (also known as repulsive mode) AFMs, and cyclical mode AFMs (periodically referred to herein as TappingMode(trademark) AFMs.)
The contact mode AFM is described in detail in Hansma. Generally, the contact mode AFM is characterized by a probe having a bendable cantilever and a tip. The AFM operates by placing the tip directly on a sample surface and then scanning the surface laterally. When scanning, the cantilever bends in response to sample surface height variations, which are then monitored by an AFM deflection detection system to map the sample surface. The deflection detection system of such contact mode AFMs is typically an optical beam system, as described in Hansma.
Typically, the height of the fixed end of the cantilever relative to the sample surface is adjusted with feedback signals that operate to maintain a predetermined amount of cantilever bending during lateral scanning. This predetermined amount of cantilever bending has a desired value, called the setpoint. Typically, a reference signal for producing the setpoint amount of cantilever bending is applied to one input of a feedback loop. By applying the feedback signals generated by the feedback loop to an actuator within the system, and therefore adjusting the relative height between the cantilever and the sample, cantilever deflection can be kept constant at the setpoint value. By plotting the adjustment amount (as obtained by monitoring the feedback signals applied to maintain cantilever bending at the setpoint value) versus lateral position of the cantilever tip, a map of the sample surface can be created.
The second general category of AFMs, i.e., cyclical mode or TappingMode(trademark) AFMs, utilize oscillation of a cantilever to, among other things, reduce the forces exerted on a sample during scanning. In contrast to contact mode AFMs, the probe tip in cyclical mode makes contact with the sample surface or otherwise interacts with it only intermittently as the tip is scanned across the surface. Cyclical mode AFMs are described in U.S. Pat. Nos. 5,226,801, 5,412,980 and 5,415,027 by Elings et al.
In U.S. Pat. No. 5,412,980, a cyclical mode AFM is disclosed in which a probe is oscillated at or near a resonant frequency of the cantilever. When imaging in cyclical mode, there is a desired tip oscillation amplitude associated with the particular cantilever used, similar to the desired amount of cantilever deflection in contact mode. This desired amplitude of cantilever oscillation is typically kept constant at a desired setpoint value. In operation, this is accomplished through the use of a feedback loop having a setpoint input for receiving a signal corresponding to the desired amplitude of oscillation. The feedback circuit servos the vertical position of either the cantilever mount or the sample by applying a feedback control signal to a Z actuator so as to cause the probe to follow the topography of the sample surface.
Typically, the tip""s oscillation amplitude is set to be greater than 20 nm peak-to-peak to maintain the energy in the cantilever arm at a much higher value than the energy that the cantilever loses in each cycle by striking or otherwise interacting with the sample surface. This provides the added benefit of preventing the probe tip from sticking to the sample surface. Ultimately, to obtain sample height data, cyclical mode AFMs monitor the Z actuator feedback control signal that is produced to maintain the established setpoint. A detected change in the oscillation amplitude of the tip and a resulting feedback control signal are indicative of a particular surface topography characteristic. By plotting these changes versus the lateral position of the cantilever, a map of the surface of the sample can be generated.
Notably, AFMs have become accepted as a useful metrology tool in manufacturing environments in the integrated circuit and data storage industries. A limiting factor to the more extensive use of the AFM is the limited throughput per machine due to the slow imaging rates of AFMs relative to competing technologies. Although it is often desirable to use an AFM to measure surface topography of a sample, the speed of the AFM is typically far too slow for production applications. For instance, in most cases, AFM technology requires numerous machines to keep pace with typical production rates. As a result, using AFM technology for surface measurement typically yields a system that has a high cost per measurement. A number of factors are responsible for these drawbacks associated with AFM technology, and they are discussed generally below.
AFM imaging, in essence, typically is a mechanical measurement of the surface topography of a sample such that the bandwidth limits of the measurement are mechanical ones. An image is constructed from a raster scan of the probe over the area to be imaged. In both contact and cyclical mode, the tip of the probe is caused to scan across the sample surface at a velocity equal to the product of the scan size and the scan frequency. As discussed previously, the height of the fixed end of the cantilever relative to the sample surface can be adjusted during scanning at a rate typically much greater than the scanning rate in order to maintain a constant force (contact mode) or oscillation amplitude (cyclical mode) relative to the sample surface.
Notably, the bandwidth requirement for a particular application of a selected cantilever is generally predetermined. Therefore, keeping in mind that the bandwidth of the height adjustment (hereinafter referred to as the Z axis or Z-position bandwidth) is dependent upon the tip velocity as well as the sample topography, the required Z-position bandwidth typically limits the maximum scan rate for a given sample topography.
Further, the bandwidth of the AFM in these feedback systems is usually lower than the open loop bandwidth of any one component of the system. In particular, as the 3 dB roll-off frequency of any component is approached, the phase of the response is retarded significantly before any loss in amplitude response. The frequency at which the total phase lag of all the components in the system is large enough for the loop to be unstable is the ultimate bandwidth limit of the loop. When designing an AFM, although the component of the loop which exhibits the lowest response bandwidth typically demands the focus of design improvements, reducing the phase lag in any part of the loop will typically increase the bandwidth of the AFM as a whole.
With particular reference to the contact mode AFM, the bandwidth of the cantilever deflection detection apparatus is limited by a mechanical resonance of the cantilever due to the tip""s interaction with the sample. This bandwidth increases with the stiffness of the cantilever. Notably, this stiffness can be made high enough such that the mechanical resonance of the cantilever is not a limiting factor on the bandwidth of the deflection detection apparatus, even though sensitivity to increased imaging forces may be compromised.
Nevertheless, in contact mode, the Z position actuator still limits the Z-position bandwidth. Notably, Z position actuators for AFMs are typically piezo-tube or piezo-stack actuators which are selected for their large dynamic range and high sensitivity. Such devices generally have a mechanical resonance far below that of the AFM cantilever brought in contact with the sample, typically around 1 kHz, thus limiting the Z-position bandwidth.
Manalis et al. (Manalis, Minne, and Quate, xe2x80x9cAtomic force microscopy for high speed imaging using cantilevers with an integrated actuator and sensor,xe2x80x9d Appl. Phys. Lett., 68 (6) 871-3 (1996)) demonstrated that contact mode imaging can be accelerated by incorporating the Z position actuator into the cantilever beam. A piezoelectric film such as ZnO was deposited on the tip-side of the cantilever. The film causes the cantilever to act as a bimorph such that by applying a voltage dependent stress, the cantilever will bend. This bending of the cantilever, through an angle of one degree, or even less, results in microns of Z positioning range. Further, implementing the Z position actuator in the cantilever increases the Z-position bandwidth of the contact mode AFM by more than an order of magnitude.
Nevertheless, such an AFM exhibits new problems with the Z positioning which were not concerns with other known AFMs. For instance, the range of the Z actuator integrated with the cantilever is less than is required for imaging many AFM samples. In addition, because the positioning sensitivity of each cantilever is different, the AFM requires recalibration whenever the probe is changed due to a worn or broken tip. Further, the sensitivity in some cases exhibits undesirable non-linearity at low frequencies. These problems can make the Z actuator integrated with the cantilever a less than optimal choice for general use as the Z actuator in commercial AFMs.
Furthermore, notwithstanding the above, in many AFM imaging applications, the use of contact mode operation is unacceptable. Friction between the tip and the sample surface can damage imaged areas as well as degrade the tip""s sharpness. Therefore, for many of the applications contemplated by the present invention, the preferred mode of operation is cyclical mode, i.e., TappingMode(trademark). However, the bandwidth limitations associated with cyclical mode detection are typically far greater than those associated with contact mode operation.
In cyclical or non-continuous contact mode operation, the AFM cantilever is caused to act as a resonant beam in steady state oscillation. When a force is applied to the cantilever, the force can be measured as a change in either the oscillation amplitude or frequency. One potential problem associated with cyclical mode operation is that the bandwidth of the response to this force is proportional to 1/Q (where Q is the xe2x80x9cquality factorxe2x80x9d of the natural resonance peak), while the force sensitivity of the measurement is proportional to the Q of the natural resonance peak. Because, in many imaging applications, the bandwidth is the primary limiting factor of scan rate, the Q is designed to be low to allow for increased imaging speeds. However, reducing the Q of the cantilever correspondingly reduces force detection sensitivity, which thereby introduces noise into the AFM image.
A further contributing factor to less than optimal scan rates in cyclical mode operation is the fact that the amplitude error signal has a maximum magnitude. Over certain topographical features, a scanning AFM tip will pass over a dropping edge. When this occurs, the oscillation amplitude of the cantilever will increase to the free-air amplitude, which is not limited by tapping on the surface. The error signal of the control loop is then the difference between the free-air amplitude and the set point amplitude. In this instance, the error signal is at a maximum and will not increase with a further increase in the distance of the tip from the sample surface. The topography map will be distorted correspondingly.
Finally, the maximum gain of the control loop in cyclical mode is limited by phase shifts, thus further limiting the loop bandwidth. In view of these drawbacks, the Z position measurement for an atomic force microscope is typically characterized as being slew rate limited by the product of the maximum error signal and the maximum gain.
As a result, AFM technology posed a challenging problem if the scan rate in cyclical mode was to be increased significantly. One general solution proposed by Mertz et al. (Mertz, Marti, and Mlynek, xe2x80x9cRegulation of a microcantilever response by force feedback,xe2x80x9d Appl. Phys. Lett. 62 (19) at 2344-6 (1993)) (hereinafter xe2x80x9cMertzxe2x80x9d), but not directed to existing cyclical mode AFMs, included a method for decreasing the effective Q of a cantilever while preserving the sensitivity of the natural resonance. In this method, a feedback loop is applied to the cantilever resonance driver such that the amplitude of the driver to the cantilever is modified based on the measured response of the cantilever. This technique serves to modify the effective Q of the resonating cantilever and will be referred to hereinafter as xe2x80x9cactive damping.xe2x80x9d Mertz accomplished active damping by thermally exciting the cantilever by first coating the cantilever with a metal layer that had different thermal expansion properties than the cantilever beam itself. Then, in response to the feedback signals, Mertz modulated a laser incident on the cantilever, so as to apply a modified driving force.
When active damping is applied to the Mertz structure, mechanical resonances other than that of the cantilever are excited, and the gain of the active damping feedback cannot be increased enough to significantly modify the effective cantilever Q. Further, the Mertz design is prohibitively inflexible for systems contemplated by the present invention due to the fact that, among other things, the modulating laser only deflects the cantilever in one direction. This introduces a frequency doubling effect that must be accounted for to process the output. Overall, the Mertz system is complex and produces marginally reliable measurements at undesirably slow speeds.
In previous embodiments of the invention, an AFM with a Z position actuator and a self-actuated Z position cantilever (both operable in cyclical mode and contact mode), was implemented with appropriately nested feedback control circuitry to achieve high-speed imaging and accurate Z position measurements. The feedback signals applied to each of the actuators are independently monitored to indicate the topography of the sample surface, depending upon the scan rate and sample topography. Further, the feedback system can modify the effective Q of a resonating cantilever without exciting mechanical resonance""s other than that of the cantilever. As a result, the system can optimize the Z-position bandwidth of the cantilever response to maximize scanning/imaging speeds, yet preserve instrument sensitivity.
Notably, however, the AFM cantilever is typically a consumable part of the system. The AFM cantilever tip wears out during the course of normal usage and must be frequently replaced. Each time a new AFM cantilever is introduced to the system, the driving oscillator must be adjusted to the natural resonance of the cantilever. In the previous embodiments of the Q modifying circuit, the cantilever is driven not only by the oscillator, but also by a filtered function of its own deflection. For each new cantilever, the transfer function of the Q modifying filter must be adjusted to optimize the response of the cantilever. This adjustment can be difficult to automate and typically requires either extensive computer processing or the intervention of an expert user.
The preferred embodiment of the present invention increases the speed and ease of use of an AFM by including an amplitude detection circuit to dynamically control the cantilever drive signal in the amplitude domain. In particular, by demodulating the cantilever response before it is used to modify the drive signal to the cantilever, the need to adjust the transfer function of a Q modifying filter in the feedback path is eliminated, thus making operation more cost-effective, efficient, and allowing ready substitution of different cantilevers.
Similar to previous embodiments, the present invention preferably combines an AFM Z position actuator and a self-actuated Z position cantilever (both operable in cyclical mode and contact mode), with appropriately nested feedback control circuitry to achieve high-speed imaging and accurate Z position measurements. The feedback signals applied to each of the actuators can be independently monitored to indicate the topography of the sample surface, depending upon the scan rate and sample topography.
According to another aspect, the lower frequency topography features of a sample, including the slope of the sample surface, are followed by a standard Z actuator while the high frequency components of the surface topography are followed by the self-actuated cantilever. Preferably, two feedback loops are employed. The first feedback loop controls the self-actuated cantilever to maintain a relatively constant force between the tip of the cantilever and the sample surface. The second feedback loop controls the standard Z actuator, at a lower speed than the first feedback loop and serves either (1) to keep the self-actuated cantilever within its operating Z range or (2) to maintain the linearity of the positioning sensitivity of the cantilever when following low frequency topography. This embodiment also allows for the standard Z actuator to be exclusively used for accurate height measurements when the scan rate is sufficiently lowered, typically less than 500 xcexcm/sec.
According to a preferred embodiment, an AFM which operates in cyclical mode (i.e., TappingMode(trademark)) combines both the AFM Z actuator and the self-actuated cantilever with appropriate feedback control in a system that oscillates the self-actuated actuator without introducing mechanical resonance""s other than that of the cantilever. Most notably, in this preferred embodiment, the self-actuated cantilever is not oscillated by vibrating a piezo-crystal mechanically coupled to the cantilever, but rather is oscillated at its resonance by directly exciting the piezoelectric material disposed thereon. This eliminates mechanical resonance""s in the coupling path which would otherwise be present.
As suggested above, the speed of a standard AFM in cyclical mode is generally limited by the loop bandwidth of the force detection circuitry and the Z positioning apparatus. A further limiting factor associated with standard AFMs pertains to phase shift contributions from the various components of the loop that accumulate to limit the gain of an otherwise stable operating system. Importantly, however, the self-actuated cantilever does not have significant phase shift contributions at standard operating frequencies, even though the detection bandwidth of the AFM in cyclical mode is still limited by the width of the resonance peak of the cantilever. Therefore, the self-actuated cantilever feedback loop is considerably faster than the AFM Z position actuator feedback loop, when both are limited by the same detection bandwidth. Notably, however, this embodiment also increases the speed of the AFM Z actuator feedback loop by providing a larger error signal than that which is generated by the cyclical mode amplitude deflection detector.
Next, the combination of the standard AFM Z actuator and the self-actuated cantilever allows for greater flexibility in fast scanning cyclical mode. When the Z actuator feedback loop is disabled or operating with low gain, the topography appears as the control signal to the self-actuated cantilever. This control signal preferably also serves as the error signal for the second or AFM Z actuator feedback loop. When the gain of the second feedback loop is optimized, i.e., when the Z actuator is operating as fast as possible without yielding unreliable output, the topography then appears in the control signal for the AFM Z position actuator. As a result, by incorporating the self-actuated cantilever within the control loop, the speed of obtaining highly accurate sample characteristic measurements can be increased. Also, as in previous embodiments, the standard Z actuator can be used to remove slope or non-linearities from the scan in the case in which the self-actuated cantilever follows the topography of the sample surface. Further, as an alternative to a standard Z actuator such as a piezo-stack actuator, a thermal actuator disposed on the self-actuated cantilever can be used.
Another preferred embodiment uses the integrated piezoelectric element of a self-actuated cantilever to modify the Q of the mechanical resonance of the cantilever. In operation, the cantilever resonance preferably is excited with the integrated piezoelectric element, rather than with a mechanically coupled driving piezo-crystal. The circuit which provides the cantilever drive signal modifies the Q of the lever with feedback from the detected deflection signal.
In particular, according to one preferred embodiment, the deflection signal is phase shifted, preferably by 90 degrees, and added back to the cantilever drive signal. This feedback component of the drive signal modifies the damping of the cantilever resonance (i.e., active damping) and thereby controllably decreases or enhances the Q. Alternatively, the deflection signal can be fed to a differentiator to modify the Q of the mechanical resonance of the cantilever. The differentiated signal is added back to the cantilever drive signal as a feedback signal to provide the active damping. Notably, in this alternative embodiment, the Q can be modified to provide active enhancement, for example, to increase the sensitivity of the response. When modification of the cantilever Q is combined with the structure of the previously described embodiment wherein the self-actuated cantilever is used for Z positioning in synchronicity with an AFM Z position actuator, the scan speed of the AFM in cyclical mode can be increased by an order of magnitude or more.
Moreover, in an effort to avoid the negative effects associated with positive feedback in the system (described below), a preferred embodiment of the present invention may include a bandpass filter centered around the peak of desirable operation. The filter is preferably disposed at the output of the cantilever drive circuit so as to insure that the system damps the peak, thus allowing the system to achieve damping up to a factor of, for example, a hundred, rather than a maximum factor of fifty with the above-described systems.
Further, although the system described immediately above achieves significant damping by insuring that the peak is damped, because each cantilever may have a different resonant frequency, the phase shifter included in the damping feedback circuit will have to be adjusted. It is desirable to not have to account for differences in cantilevers that will be used with the system. All filters (for example, the just-described bandpass filter) have a phase shift associated with them. Such a phase shift typically must be quantified and accounted for, and that can be accomplished in the phase shifter for a particular frequency cantilever. However, making adjustments to the phase shifter each time a cantilever is replaced is tedious and thus does not lend itself well to current high throughput demands.
As a result, in another preferred embodiment of the invention, the imaging dynamics are modified by an active drive technique to optimize the bandwidth of amplitude detection. The deflection is preferably measured by an optical detection system including a laser and a photodetector, which measures cantilever deflection by an optical beam bounce technique or another conventional technique. The detected deflection of the cantilever is subsequently demodulated to give a signal proportional to the amplitude of oscillation of the cantilever, which is used to drive the cantilever. Note that one advantage of this preferred embodiment is that the self-actuated probe is not required for the dynamic drive circuit to be effective. For example, if a piezo-crystal mechanically coupled to the cantilever is employed to drive the cantilever, any resonances introduced thereby will not affect the active damping because the active damping circuitry is operating in the amplitude domain and thus does not have to compensate for frequency effects. This is contrary to the previous active damping embodiments which operate in the frequency domain. As a result, the performance of the active damping of the AFM cantilever of the present embodiment is not considerably reduced when the cantilever is not the self-actuated type.
Continuing, as described with respect to tapping mode imaging, a desired operating amplitude of the cantilever oscillation is represented by the amplitude setpoint. The amplitude setpoint is subtracted from the demodulated amplitude signal to generate a deflection amplitude error signal. This amplitude error signal is then used to scale the drive signal to the cantilever. In particular, this embodiment typically drives the cantilever with some nominal steady state amplitude and adds to that drive, a dynamic drive amplitude which is proportional to the deflection amplitude error signal.
For increased speed, the drive amplitude is controlled with negative feedback from the deflection amplitude error signal. When the probe moves toward the sample surface, the response amplitude of the probe will naturally decrease, giving a negative decreasing amplitude error signal. The dynamic drive feedback will then increase the drive to the cantilever. While scanning, the probe tip may encounter an upward going step, for example. The oscillation amplitude of the cantilever will be limited by the sample surface to a lower RMS value. The Z position feedback loop responds by moving the probe away from the surface. This is the point at which more drive amplitude is required such that the cantilever tip will continue to tap on the surface. Since the RMS amplitude is reduced, the dynamic drive circuit will be supplying the cantilever with increased drive signal amplitude to meet that need.
For gentler imaging, the drive amplitude is controlled with positive feedback from the deflection amplitude error signal. When the probe moves further away from the sample surface, the response amplitude of the probe will naturally increase, giving a positive or increasing amplitude error signal. The dynamic drive feedback will increase the drive to the cantilever to maintain tapping of the tip on the surface. When the probe moves towards the sample surface, the response amplitude of the probe will be limited by the sample surface and forced to decrease, giving a negative decreasing amplitude error signal. The dynamic drive feedback will decrease the drive to the cantilever to prevent it from tapping on the surface with excess force.
The amplitude error signal is an indication of the changing position of the probe tip with respect to the sample surface. It is used by the Z position feedback loop to maintain the probe tip in close proximity to the sample surface. The speed of the Z feedback loop is increased if the amplitude error signal is utilized to determine when the cantilever will require more drive signal amplitude in order for the Z position feedback loop to respond quickly to topographic changes.
These and other objects, features, and advantages of the invention will become apparent to those skilled in the art from the following detailed description and the accompanying drawings. It should be understood, however, that the detailed description and specific examples, while indicating preferred embodiments of the present invention, are given by way of illustration and not of limitation. Many changes and modifications may be made within the scope of the present invention without departing from the spirit thereof, and the invention includes all such modifications.